Complexity - A Guided Tour Part 18

FIGURE 18.1. Ill.u.s.tration of genetic "switches." (a) A DNA sequence, containing a switch with two signature subsequences, a functional gene turned on by that switch, and two regulatory master genes. The regulatory master genes give rise to regulatory proteins. (b) The regulatory proteins bind to the signature subsequences, switching on the functional gene-that is, allowing it to be transcribed.

Where do these special regulator proteins come from? Like all proteins, they come from genes, in this case regulatory genes that encode such proteins in order to turn other genes on or off, depending on the current state of the cell. How do these regulatory genes determine the current state of the cell? By the presence or absence of proteins that signal the state of the cell by binding to the regulatory genes' own switches. Such proteins are often encoded by other regulatory genes, and so forth.

In summary, genetic regulatory networks are made up of several different kinds of ent.i.ties, including functional genes that encode proteins (and sometimes noncoding RNA) for cellular maintenance or building, and regulatory genes that encode proteins (and sometimes noncoding RNA) that turn other genes on or off by binding to DNA "switches" near to the gene in question.

I can now give Evo-Devo's answers to the three questions posed at the beginning of this section. Humans (and other animals) can be more complex than their number of genes would suggest for many reasons, some listed above in the "What Is a Gene" section. But a primary reason is that genetic regulatory networks allow a huge number of possibilities for gene expression patterns, since there are so many possible ways in which proteins can be attached to switches.

The reason we humans can share so many genes with other creatures quite different from us is that, although the genes might be the same, the sequences making up switches have often evolved to be different. Small changes in switches can produce very different patterns of genes turning on and off during development. Thus, according to Evo-Devo, the diversity of organisms is largely due to evolutionary modifications of switches, rather than genes. This is also the reason that large changes in morphology-possibly including speciation-can happen swiftly in evolutionary time: the master genes remain the same, but switches are modified. According to Evo-Devo, such modifications-in the parts of DNA long thought of as "junk"-are the major force in evolution, rather than the appearance of new genes. Biologist John Mattick goes so far as to say, "The irony ... is that what was dismissed as junk [DNA] because it wasn't understood will turn out to hold the secret of human complexity."

One striking instance of Evo-Devo in action is the famous example of the evolution of finches' beaks. As I described in chapter 5, Darwin observed large variations in beak size and shape among finches native to the Galapagos Islands. Until recently, most evolutionary biologists would have a.s.sumed that such variations resulted from a gradual process in which chance mutations of several different genes acc.u.mulated. But recently, a gene called BMP4 was discovered that helps control beak size and shape by regulating other genes that produce bones. The more strongly BMP4 is expressed during the birds' development, the larger and stronger their beaks. A second gene, called calmodulin, was discovered to be a.s.sociated with long, thin beaks. As Carol Kaesuk Yoon reported in the New York Times, "To verify that the BMP4 gene itself could indeed trigger the growth of grander, bigger, nut-crushing beaks, researchers artificially cranked up the production of BMP4 in the developing beaks of chicken embryos. The chicks began growing wider, taller, more robust beaks similar to those of a nut-cracking finch .... As with BMP4, the more that calmodulin was expressed, the longer the beak became. When scientists artificially increased calmodulin in chicken embryos, the chicks began growing extended beaks, just like a cactus driller .... So, with just these two genes, not tens or hundreds, the scientists found the potential to re-create beaks, ma.s.sive or stubby or elongated." The conclusion is that large changes in the morphology of beaks (and other traits) can take place rapidly without the necessity of waiting for many chance mutations over a long period of time.

Another example where Evo-Devo is challenging long-held views about evolution concerns the notion of convergent evolution. In my high school biology cla.s.s, we learned that the octopus eye and the human eye-greatly different in morphology-were examples of convergent evolution: eyes in these two species evolved completely independently of one another as a consequence of natural selection acting in two different environments in which eyes were a useful adaptation.

However, recent evidence has indicated that the evolution of these two eyes was not as independent as previously thought. Humans, octopi, flies, and many other species have a common gene called PAX6, which helps direct the development of eyes. In a strange but revealing experiment, the Swiss biologist Walter Gehring took PAX6 genes from mice and inserted them into the genomes of fruit flies. In particular, in different studies, PAX6 was inserted in three different parts of the genome: those that direct the development of legs, wings, and antennae, respectively. The researchers got eerie results: eye-like structures formed on flies' legs, wings, and antennae. Moreover, the structures were like fly eyes, not mouse eyes. Gehring's conclusion: the eye evolved not many times independently, but only once, in a common ancestor with the PAX6 gene. This conclusion is still quite controversial among evolutionary biologists.

Although genetic regulatory networks directed by master genes can produce great diversity, they also enforce certain constraints on evolution. Evo-Devo scientists claim that the types of body morphology (called body plans) any organism can have are highly constrained by the master genes, and that is why only a few basic body plans are seen in nature. It's possible that genomes vastly different from ours could result in new types of body plans, but in practice, evolution can't get us there because we are so reliant on the existing regulatory genes. Our possibilities for evolution are constrained. According to Evo-Devo, the notion that "every trait can vary indefinitely" is wrong.

Genetic Regulation and Kauffman's "Origins of Order".

Stuart Kauffman is a theoretical biologist who has been thinking about genetic regulatory networks and their role in constraining evolution for over forty years, long before the ascendency of Evo-Devo. He has also thought about the implications for evolution of the "order" we see emerging from such complex networks.

Kauffman is a legendary figure in complex systems. My first encounter with him was at a conference I attended during my last year of graduate school. His talk was the very first one at the conference, and I must say that, for me at the time, it was the most inspiring talk I had ever heard. I don't remember the exact topic; I just remember the feeling I had while listening that what he was saying was profound, the questions he was addressing were the most important ones, and I wanted to work on this stuff too.

Kauffman started his career with a short stint as a physician but soon moved to genetics research. His work was original and influential; it earned him many academic accolades, including a MacArthur "genius" award, as well as a faculty position at the Santa Fe Inst.i.tute. At SFI seminars, Kauffman would sometimes chime in from the audience with, "I know I'm just a simple country doctor, but ... " and would spend a good five minutes or more fluently and eloquently giving his extemporaneous opinion on some highly technical topic that he had never thought about before. One science journalist called him a "world-cla.s.s intellectual riffer," which is an apt description that I interpret as wholly complimentary.

Stuart Kauffman (Photograph by Daryl Black, reprinted with permission.).

Stuart's "simple country doctor" humble affect belies his personality. Kauffman is one of Complex Systems' big thinkers, a visionary, and not what you would call a "modest" or "humble" person. A joke at SFI was that Stuart had "patented Darwinian evolution," and indeed, he holds a patent on techniques for evolving protein sequences in the laboratory for the purpose of discovering new useful drugs.

RANDOM BOOLEAN NETWORKS.

Kauffman was perhaps the first person to invent and study simplified computer models of genetic regulatory networks. His model was a structure called a Random Boolean Network (RBN), which is an extension of cellular automata. Like any network, an RBN consists of a set of nodes and links between the nodes. Like a cellular automaton, an RBN updates its nodes' states in discrete time steps. At each time step each node can be in either state on or state off.

FIGURE 18.2. (a) A random Boolean network with five nodes. The in-degree (K) of each node is equal to 2. At time step 0, each node is in a random initial state: on (black) or off (white). (b) Time step 1 shows the network after each node has updated its state.

The property that on and off are the only allowed states is where the term Boolean comes in: a Boolean rule (or function) is one that gets some number of inputs, each equal to either 0 or 1, and from those inputs it produces an output of a 0 or 1. Such rules are named after the mathematician George Boole, who did extensive mathematical research on them.

In an RBN, links are directional: if node A links to node B, node B does not necessarily (but can possibly) link to node A. The in-degree of each node (the number of links from other nodes to that node) is the same for each node-let's call that number K.

Here is how to build an RBN: for each node, create in-links to that node from K other randomly chosen nodes (including, possibly, a self-link), and give that node a Boolean rule, chosen randomly, that inputs K on or off states and outputs a single on or off state (figure 18.2a).

To run the RBN, give each node an initial state of on or off chosen at random. Then at each time step, each node transmits its state to the nodes it links to, and receives as input the states from the nodes that link to it. Each node then applies its rule to its input to determine its state at the next time step. All this is ill.u.s.trated in figure 18.2, which shows the action of an RBN of five nodes, each with two inputs, over one time step.

RBNs are similar to cellular automata, but with two major differences: nodes are connected not to spatially neighboring nodes but at random, and rather than all nodes having an identical rule, each node has its own rule.

In Kauffman's work, the RBN as a whole is an idealized model of a genetic regulatory network, in which "genes" are represented by nodes, and "gene A regulates gene B" is represented by node A linking to node B. The model is of course vastly simpler than real genetic networks. Using such idealized models in biology is now becoming common, but when Kauffman started this work in the 1960s, it was less well accepted.

LIFE AT THE EDGE OF CHAOS.

Kauffman and his students and collaborators have done a raft of simulations of RBNs with different values of the in-degree K for each node. Starting from a random initial state, and iterated over a series of time steps, the nodes in the RBN change state in random ways for a while, and finally settle down to either a fixed point (all nodes' states remain fixed) or an oscillation (the state of the whole network oscillates with some small period), or do not settle down at all, with random-looking behavior continuing over a large number of iterations. Such behavior is chaotic, in that the precise trajectory of states of the network have sensitive dependence on the initial state of the network.

Kauffman found that the typical final behavior is determined by both the number of nodes in the network and each node's in-degree K. As K is increased from 1 (i.e., each node has exactly one input) all the way up to the total number of nodes (i.e., each node gets input from all other nodes, including itself), the typical behavior of the RBNs moves through the three different "regimes" of behavior (fixed-point, oscillating, chaotic). You might notice that this parallels the behavior of the logistic map as R is increased (cf. chapter 2). At K = 2 Kauffman found an "interesting" regime-neither fixed point, oscillating, or completely chaotic. In a.n.a.logy with the term "onset of chaos" used with the logistic map, he called this regime the "edge of chaos."

a.s.suming the behavior of his RBNs reflected the behavior of real genetic networks, and making an a.n.a.logy with the phases of water as temperature changes, he concluded that "the genomic networks that control development from zygote to adult can exist in three major regimes: a frozen ordered regime, a gaseous chaotic regime, and a kind of liquid regime located in the region between order and chaos."

Kauffman reasoned that, for an organism to be both alive and stable, the genetic networks his RBNs modeled had to be in the interesting "liquid" regime-not too rigid or "frozen," and not too chaotic or "gaseous." In his own words, "life exists at the edge of chaos."

Kauffman used the vocabulary of dynamical systems theory-attractors, bifurcations, chaos-to describe his findings. Suppose we call a possible configuration of the nodes' states a global state of the network. Since RBNs have a finite number of nodes, there are only a finite number of possible global states, so if the network is iterated for long enough it will repeat one of the global states it has already been in, and hence cycle through the next series of states until it repeats that global state again. Kauffman called this cycle an "attractor" of the network. By performing many simulations of RBNs, he estimated that the average number of different attractors produced in different networks with K = 2 was approximately equal to the square root of the number of nodes.

Next came a big leap in Kauffman's interpretation of this model. Every cell in the body has more or less identical DNA. However, the body has different types of cells: skin cells, liver cells, and so forth. Kauffman a.s.serted that what determines a particular cell type is the pattern of gene expression in the cell over time-I have described above how gene expression patterns can be quite different in different cells. In the RBN model, an attractor, as defined above, is a pattern over time of "gene expression." Thus Kauffman proposed that an attractor in his network represents a cell type in an organism's body. Kauffman's model thus predicted that for an organism with 100,000 genes, the number of different cell types would be approximately the square root of 100,000, or 316. This is not too far from the actual number of cell types identified in humans-somewhere around 256.

At the time Kauffman was doing these calculations, it was generally believed that the human genome contained about 100,000 genes (since the human body uses about 100,000 types of proteins). Kauffman was thrilled that his model had come close to correctly predicting the number of cell types in humans. Now we know that the human genome contains only about 25,000 genes, so Kauffman's model would predict about 158 cell types.

THE ORIGIN OF ORDER.

The model wasn't perfect, but Kauffman believed it ill.u.s.trated his most important general point about living systems: that natural selection is in principle not necessary to create a complex creature. Many RBNs with K = 2 exhibited what he termed "complex" behavior, and no natural selection or evolutionary algorithm was involved. His view was that once a network structure becomes sufficiently complex-that is, has a large number of nodes controlling other nodes-complex and "self-organized" behavior will emerge. He says, Most biologists, heritors of the Darwinian tradition, suppose that the order of ontogeny is due to the grinding away of a molecular Rube Goldberg machine, slapped together piece by piece by evolution. I present a countering thesis: most of the beautiful order seen in ontogeny is spontaneous, a natural expression of the stunning self-organization that abounds in very complex regulatory networks. We appear to have been profoundly wrong. Order, vast and generative, arises naturally.

Kauffman was deeply influenced by the framework of statistical mechanics, which I described in chapter 3. Recall that statistical mechanics explains how properties such as temperature arise from the statistics of huge numbers of molecules. That is, one can predict the behavior of a system's temperature without having to follow the Newtonian trajectory of every molecule. Kauffman similarly proposed that he had found a statistical mechanics law governing the emergence of complexity from huge numbers of interconnected, mutually regulating components. He termed this law a "candidate fourth law of thermodynamics." Just as the second law states that the universe has an innate tendency toward increasing entropy, Kauffman's "fourth law" proposes that life has an innate tendency to become more complex, which is independent of any tendency of natural selection. This idea is discussed at length in Kauffman's book, The Origins of Order. In Kauffman's view, the evolution of complex organisms is due in part to this self-organization and in part to natural selection, and perhaps self-organization is really what predominates, severely limiting the possibilities for selection to act on.

Reactions to Kauffman's Work.

Given that Kauffman's work implies "a fundamental reinterpretation of the place of selection in evolutionary theory," you can imagine that people react rather strongly to it. There are a lot of huge fans of this work ("His approach opens up new vistas"; it is "the first serious attempt to model a complete biology"). On the other side, many people are highly skeptical of both his results and his broad interpretations of them. One reviewer called Kauffman's writing style "dangerously seductive" and said of The Origins of Order, "There are times when the bracing walk through hypers.p.a.ce seems unfazed by the nagging demands of reality."

Indeed, the experimental evidence concerning Kauffman's claims is not all on his side. Kauffman himself admits that regarding RBNs as models of genetic regulatory networks requires many unrealistic a.s.sumptions: each node can be in only one of two states (whereas gene expression has different degrees of strength), each has an identical number of nodes that regulate it, and all nodes are updated in synchrony at discrete time steps. These simplifications may ignore important details of genetic activity.

Most troublesome for his theory are the effects of "noise"-errors and other sources of nondeterministic behavior-that are inevitable in real-world complex systems, including genetic regulation. Biological genetic networks make errors all the time, yet they are resilient-most often our health is not affected by these errors. However, simulations have shown that noise has a significant effect on the behavior of RBNs, and sometimes will prevent RBNs from reaching a stable attractor. Even some of the claims Kauffman made specifically about his RBN results are not holding up to further scrutiny. For example, recall Kauffman's claim that the number of attractors that occur in a typical network is close to the square root of the number of nodes, and his interpretation of this fact in terms of cell-types. Additional simulations have shown that the number of attractors is actually not well approximated by the square root of the number of nodes. Of course this doesn't necessarily mean that Kauffman is wrong in his broader claims; it just shows that there is considerably more work to be done on developing more accurate models. Developing accurate models of genetic regulatory networks is currently a very active research area in biology.

Summary.

Evolutionary biology is still working on answering its most important question: How does complexity in living systems come about through evolution? As we have seen in this chapter, the degree of complexity in biology is only beginning to be fully appreciated. We also have seen that many major steps are being taken toward understanding the evolution of complexity. One step has been the development of what some have called an "extended Synthesis," in which natural selection still plays an important role, but other forces-historical accidents, developmental constraints, and self-organization-are joining natural selection as explanatory tools. Evolutionists, particularly in the United States, have been under attack from religious extremists and are often on the defensive, reluctant to admit that natural selection may not be the entire story. As biologists Guy Hoelzer, John Pepper, and Eric Smith have written about this predicament: "It has essentially become a matter of social responsibility for evolutionary biologists to join the battle in defense of Darwinism, but there is a scientific cost a.s.sociated with this cultural norm. Alternative ways of describing evolutionary processes, complementary to natural selection, can elicit the same defensive posture without critical a.n.a.lysis."

Evolutionary biologist Dan McShea has given me a useful way to think about these various issues. He cla.s.sifies evolutionists into three categories: adaptationists, who believe that natural selection is primary; historicists, who give credit to historical accident for many evolutionary changes; and structuralists, such as Kauffman, who focus on how organized structure comes about even in the absence of natural selection. Evolutionary theory will be unified only when these three groups are able to show how their favored forces work as an integrated whole.

Dan also gave me an optimistic perspective on this prospect: "Evolutionary biology is in a state of intellectual chaos. But it's an intellectual chaos of a very productive kind."

PART V.

Conclusion.

I will put Chaos into fourteen lines.

And keep him there; and let him thence escape.

If he be lucky; let him twist, and ape.

Flood, fire, and demon-his adroit designs.

Will strain to nothing in the strict confines.

Of this sweet order, where, in pious rape,

I hold his essence and amorphous shape,

Till he with Order mingles and combines.

Past are the hours, the years of our duress,

His arrogance, our awful servitude:

I have him. He is nothing more nor less

Than something simple not yet understood;

I shall not even force him to confess;

Or answer. I will only make him good.

-Edna St. Vincent Millay, Mine the Harvest: A Collection of New Poems.

CHAPTER 19.

The Past and Future of the Sciences of Complexity.

IN 1995, THE SCIENCE JOURNALIST John Horgan published an article in Scientific American, arguably the world's leading popular science magazine, attacking the field of complex systems in general and the Santa Fe Inst.i.tute in particular. His article was advertised on the magazine's cover under the label "Is Complexity a Sham?" (figure 19.1).

The article contained two main criticisms. First, in Horgan's view, it was unlikely that the field of complex systems would uncover any useful general principles, and second, he believed that the predominance of computer modeling made complexity a "fact-free science." In addition, the article made several minor jabs, calling complexity "pop science" and its researchers "complexologists." Horgan speculated that the term "complexity" has little meaning but that we keep it for its "public-relations value."

To add insult to injury, Horgan quoted me as saying, "At some level you can say all complex systems are aspects of the same underlying principles, but I don't think that will be very useful." Did I really say this? I wondered. What was the context? Do I believe it? Horgan had interviewed me on the phone for an hour or more and I had said a lot of things; he chose the single most negative comment to use in his article. I hadn't had very much experience with science journalists at that point and I felt really burned.